This relates to integrated circuits including Physically Unclonable Function (PUF) circuits. A PUF circuit has behavior that is determined by random physical variations such as within the integrated circuit or within the environment of the integrated circuit. The variations may depend on operating temperature, operating voltage, stress-related changes in transistor characteristics such as due to negative bias threshold instability (NBTI), accumulated environmental radiation effects, thermal noise, or other sources of variations. Due to these variations, two PUF circuits on different integrated circuits function differently even though the logic design and manufacturing steps for both integrated circuits may be the same. PUF circuits may, for example, be used to help differentiate between integrated circuits that are otherwise identical, because outputs of the PUF circuits are different.
Examples of PUF circuits include arbiter PUFs, ring-oscillator PUFs, butterfly PUFs, and static random access memory (SRAM) PUFs. These PUF circuits depend on variations in P-type and N-type transistors to produce different functionality. In general, they are dependent on gate-threshold variations in the P-type and N-type transistors. For example, variations in the gate threshold voltage of transistors in delay-based PUFs such as arbiter and ring oscillator PUF circuits change rising-edge and falling-edge path delays.
Threshold voltages and drive strengths of P-type and N-type transistors do not precisely track over all changes in operating conditions. For example, P-type and N-type transistors may exhibit different responses to changes in operating temperature and voltage. In addition, P-type and N-type transistors have different aging characteristics that affect transistor operations over the lifetime of the transistors. For example, negative bias threshold instability (NBTI) that affects P-type transistors is often different from, and more severe than, positive bias threshold instability (PBTI) for N-type transistors. In a scenario such as when the behavior of a PUF circuit depends on the relative strength between a P-type and an N-type transistor of nominally equal strength, the P-type transistor may be stronger than the N-type transistor under some operating conditions (e.g., producing a first output response), whereas the N-type transistor may be stronger than the P-type transistor under other operating conditions (e.g., producing a second output response). In other words, the functionality of the PUF circuit may be unstable.